The flight instructor was providing initial flight training to the non-certificated student pilot in a tailwheel-equipped airplane. The flight instructor reported that while the student pilot was landing the airplane it began veering left immediately after touchdown. The flight instructor attempted to correct the yaw and applied the brakes, but the airplane continued off the left side of the runway with the tailwheel still in the air. The airplane impacted some dirt, which resulted in a nose over and substantial damage to the airplane’s left wing, empennage, vertical stabilizer, and rudder. The flight instructor reported that there were no mechanical malfunctions or failures of the airplane that would have precluded normal operation. Additionally, the flight instructor reported that the student pilot had accumulated about 2 hours of flight experience at the time of the accident and described that she, “...was showing great aptitude with landings but I should have delayed her attempting to do so to further in her training.”